n^4+n^2+3=5

Solution for n^4+n^2+3=5 equation:

Simplifying
n4 + n2 + 3 = 5

Reorder the terms:
3 + n2 + n4 = 5

Solving
3 + n2 + n4 = 5

Solving for variable 'n'.

Reorder the terms:
3 + -5 + n2 + n4 = 5 + -5

Combine like terms: 3 + -5 = -2
-2 + n2 + n4 = 5 + -5

Combine like terms: 5 + -5 = 0
-2 + n2 + n4 = 0

Factor a trinomial.
(-2 + -1n2)(1 + -1n2) = 0

Factor a difference between two squares.
(-2 + -1n2)((1 + n)(1 + -1n)) = 0

Subproblem 1
Set the factor '(-2 + -1n2)' equal to zero and attempt to solve:

Simplifying
-2 + -1n2 = 0

Solving
-2 + -1n2 = 0

Move all terms containing n to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1n2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n2 = 0 + 2
-1n2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1n2 = 2

Divide each side by '-1'.
n2 = -2

Simplifying
n2 = -2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + n = 0 + -1
n = 0 + -1

Combine like terms: 0 + -1 = -1
n = -1

Simplifying
n = -1
Subproblem 3
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {-1, 1}